Method and apparatus for noise reduction

Abstract

A noise reducing method and associated apparatus for use in a medical radiographic imaging system wherein an image represented by an array of pixels is processed and the processed image is recorded on a recording medium or visualized on a display monitor. The processing comprises the steps of a) decomposing an original image into a sequence of detail images or into an array of coefficients representing detail strength at multiple resolution levels and a residual image, b) pixelwise attenuating the detail images or the coefficient arrays according to the locally estimated amount of relevant signal present and in accordance with an estimated noise level, c) reconstructing a processed image by accumulating detail obtained from the attenuated detail images or from the attenuated detail coefficients, and further adding the residual image.

We claim: 
     
       1. A method for reducing noise in a digital image represented by an array of pixel values by processing said image, said processing comprising the steps of: a) decomposing said image into a multiresolution representation comprising a set of detail images at multiple resolution levels and a residue,   b) estimating the noise level in each detail image or recalling said noise level from a noise table comprising predetermined typical noise level values corresponding to detail images with similar noise statistics;   c) establishing a local observation neighborhood around each pixel of each detail image and estimating local image content within said neighborhood,   d) pixelwise attenuating the detail images as a function of the estimated amount of image content and in accordance with said estimated noise level,   e) computing said processed image by applying a reconstruction algorithm to the residue and to the attenuated detail images, said reconstruction algorithm being such if it were applied to the residual image and the detail images without attenuation, then said digital image or a close approximation thereof would be obtained.   
     
     
       2. A noise reducing method according to claim 1 wherein the dynamic range of the processed image is reduced by mapping the processed image onto a desired output dynamic range according to some specified gradation curve. 
     
     
       3. A method according to claim 1 wherein said digital image is obtained by reading out a radiation image stored in a photostimulable phosphor screen. 
     
     
       4. A noise reducing method according to claim 1 wherein the multiresolution representation has a pyramidal structure, such that the number of pixels in each detail image decreases at each coarser resolution level. 
     
     
       5. A noise reducing method according to claim 1 wherein the detail image at the finest resolution level is obtained as the pixelwise difference between the original image and an image obtained by low pass filtering the original image, and wherein the successive coarser resolution level detail images are obtained by taking the pixelwise difference between two low pass filtered versions of the original image, the second filter having a smaller bandwidth than the former. 
     
     
       6. A noise reducing method according to claim 1 wherein said multiresolution decomposition comprises at least one and at most five detail images and a residue. 
     
     
       7. A noise reducing method according to claim 1 wherein the detail images at successively coarser resolution levels are obtained as the result of each of K iterations of the following steps: a) computing an approximation image at a next coarser level by applying a low pass filter to the approximation image corresponding to the current iteration, and subsampling the result in proportion to the reduction in spatial frequency bandwidth, using the original image as input to said low pass filter in the course of the first iteration;   b) computing a detail image as the pixelwise difference between the approximation image corresponding to the current iteration and the approximation image at a next coarser resolution level computed according to the method of step a) of claim 1 wherein the multiresolution representation has e pyramidal structure, such that the number of pixels in each detail image decreases at each coarser resolution level, and wherein both images are brought into register by proper interpolation of the latter image;   and wherein said residue is a residual image that is equal to the approximation image produced by the last iteration;   and wherein said processed image is computed by iterating K times the following procedure starting from the coarsest detail image and the residual image:   computing the approximation image at the current resolution level by pixelwise adding the detail image at the same resolution level to the approximation image at the coarser resolution level corresponding to the previous iteration, both images being brought into register by proper interpolation of the latter image; using the residual image instead of said coarser approximation image in the course of the first iteration.   
     
     
       8. A noise reducing method according to claim 7 wherein said subsampling is performed with a factor of 2, and said low-pass filter has an impulse response which approximates a two-dimensional gaussian distribution. 
     
     
       9. A method according to claim 1 wherein said multiresolution representation is obtained by applying a transform to said digital image yielding detail transform images at multiple resolution levels and a residual coefficient, each detail transform image comprising a set of transform coefficients expressing the relative contribution to the original image of the corresponding basis function out of a set of predetermined basis functions, each of said functions representing local detail at a specific resolution level and being non-periodic, and having zero mean value, and wherein said transform is such that there exists an inverse transform which returns the original image or a close approximation thereof when being applied to said transform coefficients and said residual coefficient. 
     
     
       10. A noise reducing method according to claim 9 wherein said basis functions are orthogonal. 
     
     
       11. A noise reducing method according to claim 10 wherein said functions are discrete wavelets. 
     
     
       12. A noise reducing method according to claim 1 wherein a loss of acuity due to the stronger noise suppression in the finer detail images or detail transform images is compensated for by pixelwise multiplying each of the detail images with a factor which is larger for the finer resolution levels than it is for the coarser levels. 
     
     
       13. A noise reducing method according to claim 12 modified in that said noise suppression functions are defined as: ##EQU5## where A is the average of the function S v .sbsb.n (v)' defined as: ##EQU6## where S v .sbsb.n is the noise suppression function corresponding to a noise variance v n , where v represents the local variance, and where K is a noise suppression factor which specifies the amount of noise suppression to be applied said function S v .sbsb.n ' being evaluated across the entire corresponding image, and C is a parameter within the range 0 . . . 1, which specifies the desired relative amount of compensation for acuity loss. 
     
     
       14. A noise reducing method according to claim 13 wherein said attenuated detail images are additionally converted by means of a contrast enhancing non-linear monotonically increasing odd mapping function having a slope that gradually decreases with increasing absolute argument values. 
     
     
       15. A noise reducing method according to claim 1 wherein said digital image is preprocessed in such a way that its noise characteristics are approximately uniform, additive, band-limited and have zero mean value. 
     
     
       16. A noise reducing method according to claim 15 wherein said preprocessing consists of converting pixel values of said digital image into the square root of said pixel values. 
     
     
       17. A noise reducing method according to claim 1 wherein said noise level is determined as the estimated noise variance in each detail image. 
     
     
       18. A noise reducing method according to claim 17 wherein a set of noise suppression functions are computed, each function associated with one of said detail images, said functions being monotonically non-decreasing in one variable and parametrically depending on said noise variance in a non-increasing monotonic way and said functions being positive and asymptotically reaching a maximum value equal to one and wherein each detail image is attenuated by multiplying it by the associated noise suppression function evaluated at an abscissa equal to said local detail image variance. 
     
     
       19. A noise reducing method according to claims 17 wherein said estimation of the noise variance in an image comprises the steps of: a) establishing a compact neighborhood around each pixel of said image, computing the local variance at each center pixel based on the statistics within said neighborhood, and using said local variance at every pixel to update the corresponding entry of a local variance histogram associated with said image;   b) designating the noise variance of said image as the local variance value that corresponds to the highest number of occurences within said histogram.   
     
     
       20. A noise reducing method according to claim 19 wherein said local variance is computed as the average squared value of all pixels within said neighborhood. 
     
     
       21. A noise reducing method according to claim 18 wherein said noise suppression functions are such that the statistical expected value of the noise power in the reconstructed image is minimal. 
     
     
       22. A noise reducing method according to claim 18 wherein said noise suppression functions are defined as: ##EQU7## where S v .sbsb.n is the noise suppression function corresponding to a noise variance v n , where v represents the local variance, and where K is a noise suppression factor which specifies the amount of noise suppression to be applied. 
     
     
       23. An apparatus for processing an electronic representation of an image comprising means (30) for decomposing said electronic representation into a sequence of detail images at multiple resolution levels and a residual image at a resolution level lower than the minimum of said multiple resolution levels,   means (61) for storing said detail images,   means (62-70) for estimating the noise level in each detail image or recalling said noise level from a noise table comprising predetermined typical noise level values corresponding to detail images with similar noise statistics;   means (62-66) for estimating local image content within a neighborhood around each pixel in each said detail image   means (71,73) for pixelwise attenuating each detail image as a function of said local image content in accordance with said estimated noise level,   means (34) for computing said processed image by applying a reconstruction algorithm to the residual image and the attenuated detail images, said reconstruction algorithm being such that if it were applied to the residual image and the detail images without attenuation, then an original image or a close approximation thereof would be obtained.   
     
     
       24. An apparatus according to claim 23 comprising means for reading out detail images at each resolution level from storage means (61), means (62,64) for computing the local variance of pixels in a neighborhood at each position in said detail images,   means (66) for storing said local variance pixels,   a histogram computation circuit (67) for computing at each resolution level the histogram of the computed local variance values,   a maximum locator (69) for estimating the noise variance as the variance value with the highest occurrence within said histogram,   means (71) for pixelwise computing an attenuation coefficient as a function of local variance at each pixel in said detail images, in accordance with said noise variance at the corresponding resolution level,   and a multiplier (73) for pixelwise multiplying each detail image at a particular resolution level with the corresponding attenuation coefficients.   
     
     
       25. Apparatus according to claim 23 additionally comprising an image acquisition section (1) comprising an apparatus (14-19) for reading out a radiation image stored in a photostimulable phosphor screen by scanning said screen with stimulating radiation, detecting the light emitted upon stimulation and converting the detected light into an electronic representation.